In this question, we will consider the consequences of using an unbalanced EST when performing searches. The diagram below illustrates an unbalanced example of a St. Answer the questions below. 16 10 11 12 1. What is the height of this BST2 II. What is the minimum height that a BST must have if it stores the same values as the above EST? III. If we sesh for the value 11 in the above RST hw many talkTREF SEARCH would be made? IV. It wc search for the value 12.5 in the above BST, how many calic to TREL-SEARCH would be made Acoume it's allowed to score real values in the UST. (Hint: Look carefully at the code from lectures to see how it handles the base case in the recursion) On paper: Fema BST of minimum light containing the same values as the BST above V. What is the maximum number of calls to TREE-SEARCH that would be made it we search for any number (not necessarily stored in the BSD) in the new BST? VI. Assume we're given an arbitrary BST containing the same values as the BST above and a number (which may or may not be in the BSTI. What is the smallest number k such that we can guarantee searching for in the BST would make at most k calls to TREE-SEARCH